In another screen cast the idea of reverse osmosis is described and some of the equations
are presented.
And here we just want to discuss how that driving force for permeation changes because
of a couple of factors.
1- concentration polarization and 2- because of the fact that we are permeating solvent
through a membrane, therefore changing the feed concentration of solvent.
So the idea of concentration polarization, just to review, is that we have, in this case
we will use water at the solvent, we have water plus a solute, typically like a salt,
on one side of a membrane.
Water on the other side of the membrane and the idea is that we are feeding water plus
a solute, membrane is permeable almost exclusively to water and so we end up with high purity
water on the right side of the membrane.
To do this we have high pressure.
So we have to have high pressure.
The left side overcomes the osmotic pressure.
And then the driving force is the pressure difference, so this is P1-P2, minus the osmotic
pressure and it is related to, this is the thickness, a thicker membrane will have a
lower flux, and this is a property of the membrane the permeability.
What we want to look at is what can affect this equation.
And the flux we get through a membrane.
The one of the effects is concentration polarization.
So the membrane on the feed side, because we are preferentially permeating water through
the membrane, water is permeating this direction, solute concentration, the salt concentration
is going to start to build up on the feed side because the salt now has to diffuse back
to the left because the concentration gradient of the salt, in order to equilibrate.
And we are going to have a higher concentration of the solute right at the membrane surface
because we are preferentially permeating water through the membrane.
So this is referred to as concentration polarization.
This right here, which means we have decreased the water concentration which means we have
increased the salt concentration.
A higher salt concentration means that we have a larger osmotic pressure.
Osmotic pressure increases, the salt concentration increases which means then, if we look at
our equation, if we increase the osmotic pressure in this equation then we have decreased the
driving force.
And so concentration polarization decreases the driving force during a reverse osmosis
as well as other membrane processes.
Which means if we were to calculate the flux we are not going to get the value from this
equation if we use as our osmotic pressure, won't corresponds to out here, instead now
it corresponds to what is right at the surface.
The second effect that we should be aware of is if we look at permeation while we are
feeding water plus the solute to the inside of the reverse osmosis tube.
And we have mostly water on the permeate side.
So our retentate has a higher concentration of solute.
As we move from left to right through the membrane and we preferentially permeate water
that means that we have a higher solute concentration further down the tube.
Again a higher solute concentration, this is now in the bulk of the solution.
The higher solute concentration means a higher osmotic pressure, again less driving force.
And so the flux of water through the membrane is going to be higher here than it is here,
because we have a higher concentration of water on the feed side here than we do here.
So both of these things now will decrease the amount of water we obtain for a given
feed pressure In reverse osmosis we also have the possibility, if this were a long membrane
tube or small diameter that could be a pressure drop and then the pressure here at the exit,
the pressure here is going to be lower than the pressure here.
This also will decrease the driving force for reverse osmosis.